Conventionally, an image forming system includes an image forming apparatus that forms an image on a sheet, and a sheet processing apparatus that temporarily stacks the image formed sheets on a processing tray and processes the sheet bundle, such as by stapling.
JP2004-262656 discloses that a size of a processing tray in a sheet-conveying direction is half the size of the sheet. FIGS. 22A-22C, reproduced from JP2004-262656, show a diagram in which a first sheet S is conveyed on a processing tray 540.
In FIG. 22A, a swing roller 550 is located at a position apart from a driven roller 571 on standby. The sheet discharged from an image forming apparatus is conveyed to a stacking tray 504 by a discharging roller pair 508a and 508b. 
In FIG. 22B, when the trailing end of the sheet S passes through the discharging roller pair 508a and 508b, the sheet S is held by the swing roller 550 and the driven roller 571.
In FIG. 22C, the sheet S is conveyed to a sheet trailing end stopper 562 by rotating the swing roller 550 and the driven roller 571 in a reverse direction to the sheet conveying direction. Next, the swing roller 550 moves upward to the standby position shown in FIG. 22A and the swing roller 550 prepares for a next sheet S to be discharged.
FIG. 23A shows a diagram that an after-next sheet S is conveyed on a processing tray 540.
However, in FIG. 23B, a following sheet S1 is conveyed to the sheet trailing end stopper 562 by rotating the swing roller 550 and the driven roller 571 while the following sheet S1 is rubbed on the previous sheet S. As such, the rear side of the following sheet S1 may be dirty with the image of the previous sheet S, and the image of the previous sheet S may deteriorate. This is because the following sheet S1 and the previous sheet S contact each other with a high surface pressure from the swing roller 550 and the driven roller 571.